Fractal density, scale and the modulo algebras and Arithmetics
There are 3 types of density, but the terminology can be written identically.
We first identify a form. Thn we identify a Metron suited to that form. The Metron should be precise ( Artois) and if approximate a precise Metron should be found by using Euclids algorithm( GCD, GCF,etc) this factorisation occurs first, and is a process that involves conjugation, comparison, analysis, synthesis, aggregation, division, subtraction, multiple forms of the Metron, or series of Metrons, and finally multiplication.
Those who have not read Book 7 of The Stoikeioon, will find it very instructive to do so. This is a book , within a series of books introducing basic philosophical principles of Form or Idea.
Once the Metron is suitable it may be called a monad. Monas is one singled out Metron laid down first. It is ordinal and cardinal. Ordinal first then cardinal by implication or identification with a quantity which is ordered by " size" , comparison with others from least to greatest.
So, a form is now perceivable as a mosaic of Metrons laid carefully together, continuously. Such a perception is called an Arithmos . A arrangement of Arithmoi can be ordered from least to greatest, by comparisons of the count of Metrons. These Arithmoi form a scale of sizes, each Arithmos being a quantity of magnitude, that is a size, identified by a count of Metrons .
The count, a rhythmical song becomes identified with order, size, cardinality, and also dynamic movements of the counter.
I can now establish the notion of a fractal density for a given form for a given precise Metron. The count of the Metron that completes the form is its fractal density. The reciprocal of the fractal density is a ratio:
One Metron to the fractal density eg 1 to 300.
For a fixed form the fractal density increases as the Metron becomes comparatively smaller. Thus 1 to 1200 makes sense as a reciprocal if the sizes compared are smaller, but the fractal density completes to the same or a fixed form
With a little practice, and fully aware that a fixed or standard form is referred to I can scale the size of the Metrons compared to one another. The greater the fractal density the smaller the Metron.
Now density is used in physics but in a reverse way. This time the Metron remains fixed. In this case the form expands as the count is increased. This is not density, but expansivity. However, we can use another sense , kinaesthetic , to make the sensory swap over definition. For a fixed volume as a volume Metron, a single volume is more kinaesthetically dense if to balance it more volumes of a standard volume and material have to be used.
For example a standard volume of lead requires x number of standard volumes of water . Kinaesthetic density means thawe an crossover from a bulk to a force .
Just as I can set up a kinaesthetic density I can establish an auditory density, where I balance a displacement of an elastic volume against a standard pressure displacement on this standard volume.